A Theory for Long-Memory in Supply and Demand

Santa Fe Institute Working Paper No. 04-12-041

12 Pages Posted: 30 Apr 2005

See all articles by Fabrizio Lillo

Fabrizio Lillo

Università di Bologna

Szabolcs Mike

Santa Fe Institute - Economics; Budapest University of Technology and Economics

J. Doyne Farmer

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School; Santa Fe Institute

Abstract

Recent empirical studies have demonstrated long-memory in the signs of orders to buy or sell in financial markets. We show how this can be caused by delays in market clearing. Under the common practice of order splitting, large orders are broken up into pieces and executed incrementally. If the size of such large orders is power law distributed, this gives rise to power law decaying autocorrelations in the signs of executed orders. More specifically, we show that if the cumulative distribution of large orders of volume v is proportional to v{-alpha} and the size of executed orders is constant, the autocorrelation of order signs as a function of the lag tau is asymptotically proportional to tau{-(alpha - 1)}. This is a long-memory process when alpha < 2. With a few caveats, this gives a good match to the data. A version of the model also shows long-memory fluctuations in order execution rates, which may be relevant for explaining the long-memory of price diffusion rates.

Keywords: Long memory processes, Financial markets, Order flow, Market efficiency

JEL Classification: C00, C1, G00, G1

Suggested Citation

Lillo, Fabrizio and Mike, Szabolcs and Farmer, J. Doyne, A Theory for Long-Memory in Supply and Demand. Santa Fe Institute Working Paper No. 04-12-041. Available at SSRN: https://ssrn.com/abstract=708303 or http://dx.doi.org/10.2139/ssrn.708303

Fabrizio Lillo

Università di Bologna ( email )

Via Zamboni, 33
Bologna, 40126
Italy

Szabolcs Mike

Santa Fe Institute - Economics ( email )

1399 Hyde Park Rd
Santa Fe, NM 87501
United States

Budapest University of Technology and Economics ( email )

Muegyetem rkp. 3-9
H-1111 Budapest
Hungary

J. Doyne Farmer

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School ( email )

Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

HOME PAGE: http://www.inet.ox.ac.uk/people/view/4

Santa Fe Institute ( email )

1399 Hyde Park Road
Santa Fe, NM 87501
United States
505-984-8800 (Phone)
505-982-0565 (Fax)

HOME PAGE: http://www.santafe.edu/~jdf/

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